Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#10587739 |
| commutator, socle | C2×C137 | C23×C4 |
| Fitting | #41×C137 | C4 |
| hypercenter | #41 | #10587739 |
| hypocenter | C137 | #520 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#10587739 | C2 | semidirect |
| 2. D4×#10587739 | C2 | semidirect |
| 3. #17984167 | C2 | semidirect |
| 4. C2×C4⋊#10587739 | C2 | semidirect |
| 12. #14555511 | C4 | semidirect |
| 13. #14555510 | C4 | semidirect |
| 14. #14555509 | C4 | semidirect |
| 18. #41×C137 | C4 | semidirect |
| 23. Dic274 | C2×C4 | semidirect |
| 24. D548 | C2×C4 | semidirect |
| 25. C22⋊D137 | C2×C4 | semidirect |
| 26. C2×Dic137 | C2×C4 | semidirect |
| 27. C4×D137 | C2×C4 | semidirect |
| 28. C4×D137 | C2×C4 | semidirect |
| 31. Q8×C137 | C2×C4 | semidirect |
| 32. D4×C137 | C2×C4 | semidirect |
| 33. C2×C4×C137 | C2×C4 | semidirect |
| 50. C137 | #520 | semidirect |
| 60. #41 | #10587739 | semidirect |
| 72. Q8 | C2×#10587739 | semidirect |
| 75. D4 | C2×#10587739 | semidirect |
| 84. C2×C4 | C2×#10587739 | semidirect |